A332476 -id:A332476 - cp's OEIS frontend

A332477 Numbers k that are unitary harmonic in Gaussian integers: k * A332476(k) is divisible by A332472(k) + i*A332473(k) (where i is the imaginary unit).

1, 5, 12, 50, 60, 84, 300, 420, 450, 756, 900, 1950, 3780, 7800, 9900, 33150, 49140, 54600, 100800, 132600, 265200, 491400, 928200, 1856400, 8353800, 8884200, 16707600, 52211250, 65995776, 78566400, 182739375, 183783600, 208845000, 280348992, 293046000, 329978880

Offset: 1

Amiram Eldar, Feb 13 2020

nonn

Analogous to unitary harmonic numbers (A006086), with the number and sum of unitary divisors functions generalized for Gaussian integers (A332476, A332472 + i * A332473) instead of the number and sum of unitary divisors functions (A034444, A034448).

			5 is a term since 5 * A332476(5)/(A332472(5) + i*A332473(5)) = 5 * 4/(4 + 8*i) = 1 - 2*i is a Gaussian integer.

Amiram Eldar, Table of n, a(n) for n = 1..75

Cf. A034444, A034448, A006086, A332317, A332472, A332473, A332476.

sigma[p_, e_] := If[Abs[p] == 1, 1, (p^e + 1)]; tau[p_, e_] := If[Abs[p] == 1, 1, 2]; unitaryHarmonicQ[n_] := Divisible[n * Times @@ tau @@@ (f = FactorInteger[n, GaussianIntegers -> True]), Times @@ sigma @@@ f]; Select[Range[10^5], unitaryHarmonicQ]

A239630 Factored over the Gaussian integers, the least number having n prime factors, excluding units 1, -1, i, and -i.

Original entry on oeis.org

2, 5, 10, 30, 130, 390, 2210, 6630, 46410, 192270, 1345890, 7113990, 49797930, 291673590, 2041715130

Offset: 1

T. D. Noe, Mar 31 2014

From Amiram Eldar, Jun 27 2020: (Start)
Indices of records of A086275.
Also, numbers with a record number of unitary divisors in Gaussian integers (A332476). (End)

Cf. A001221, A001222 (integer factorizations).
Cf. A078458, A086275 (Gaussian factorizations).
Cf. A239627 (number of Gaussian factors of n, including units).
Cf. A239628 (similar to this sequence, but count all prime factors).
Cf. A239629 (number of distinct factors, including units).
Cf. A332476.

nn = 12; t = Table[0, {nn}]; n = 0; found = 0; While[found < nn, n++; f = FactorInteger[n, GaussianIntegers -> True]; cnt = Length[f]; If[MemberQ[{-1, I, -I}, f[[1, 1]]], cnt--]; If[cnt <= nn && t[[cnt]] == 0, t[[cnt]] = n; found++]]; t

a(13)-a(15) from Amiram Eldar, Jun 27 2020

cp's OEIS Frontend

A332477 Numbers k that are unitary harmonic in Gaussian integers: k * A332476(k) is divisible by A332472(k) + i*A332473(k) (where i is the imaginary unit).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica